xorbits.numpy.random.noncentral_f(dfnum, dfden, nonc, size=None)[source]#

Draw samples from the noncentral F distribution.

Samples are drawn from an F distribution with specified parameters, dfnum (degrees of freedom in numerator) and dfden (degrees of freedom in denominator), where both parameters > 1. nonc is the non-centrality parameter.


New code should use the ~numpy.random.Generator.noncentral_f method of a ~numpy.random.Generator instance instead; please see the random-quick-start.

  • dfnum (float or array_like of floats) –

    Numerator degrees of freedom, must be > 0.

    Changed in version 1.14.0(numpy.random): Earlier NumPy versions required dfnum > 1.

  • dfden (float or array_like of floats) – Denominator degrees of freedom, must be > 0.

  • nonc (float or array_like of floats) – Non-centrality parameter, the sum of the squares of the numerator means, must be >= 0.

  • size (int or tuple of ints, optional) – Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if dfnum, dfden, and nonc are all scalars. Otherwise, np.broadcast(dfnum, dfden, nonc).size samples are drawn.


out – Drawn samples from the parameterized noncentral Fisher distribution.

Return type

ndarray or scalar

See also


which should be used for new code.


When calculating the power of an experiment (power = probability of rejecting the null hypothesis when a specific alternative is true) the non-central F statistic becomes important. When the null hypothesis is true, the F statistic follows a central F distribution. When the null hypothesis is not true, then it follows a non-central F statistic.



Weisstein, Eric W. “Noncentral F-Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NoncentralF-Distribution.html


Wikipedia, “Noncentral F-distribution”, https://en.wikipedia.org/wiki/Noncentral_F-distribution


In a study, testing for a specific alternative to the null hypothesis requires use of the Noncentral F distribution. We need to calculate the area in the tail of the distribution that exceeds the value of the F distribution for the null hypothesis. We’ll plot the two probability distributions for comparison.

>>> dfnum = 3 # between group deg of freedom  
>>> dfden = 20 # within groups degrees of freedom  
>>> nonc = 3.0  
>>> nc_vals = np.random.noncentral_f(dfnum, dfden, nonc, 1000000)  
>>> NF = np.histogram(nc_vals, bins=50, density=True)  
>>> c_vals = np.random.f(dfnum, dfden, 1000000)  
>>> F = np.histogram(c_vals, bins=50, density=True)  
>>> import matplotlib.pyplot as plt  
>>> plt.plot(F[1][1:], F[0])  
>>> plt.plot(NF[1][1:], NF[0])  
>>> plt.show()  

This docstring was copied from numpy.random.